English: A limit cycle is a closed trajectory in the phase space of a two-dimensional dynamical system, for which there is one or more other trajectories that approach the closed one as time tends to positive (or maybe negative) infinity. In fact, the motion corresponding to the limit cycle is established periodic oscillatory process. The well-known 16th Hilbert problem (its second part) is associated with limit cycles: for a system of two differential equations, the right side of which is polynomials in dynamic variables, it's necessary to calculate an upper bound for the number of different limit cycles in such system (the estimate may depend on the degree of the polynomials). This problem has not been solved still, even for second degree polynomials. There is an example^[1] that shows that for a system with second degree polynomials, the number of different limit cycles can reach four. This example is remarkable because the limit cycles in it have a visible normal size.
The animation shows the limit cycles from this example, in addition, it demonstrates how one of these cycles is formed (trajectories inside and outside the cycle approach it as the initial conditions changing), and also shows a comparative view of the oscillations corresponding to different cycles^[2]